An Implementation of Two-Phase Image Segmentation Using the Split Bregman Method
Olakunle Abawonse, Günay Doğan
⚠ This is a preprint. It may change before it is accepted for publication.

Abstract

In this paper, we describe an implementation of the two-phase image segmentation algorithm proposed by Goldstein, Bresson and Osher in [Geometric Applications of the Split Bregman Method: Segmentation and Surface Reconstruction, Journal of Scientific Computing, 2010]. This algorithm partitions the domain of a given 2D image into foreground and background regions, and each pixel of the image is assigned membership to one of these two regions. The underlying assumption for the segmentation model is that the pixel values of the input image can be summarized by two distinct average values, and that the region boundaries are smooth. Accordingly, the model is formulated as an energy functional whose variable is a region membership function that assigns pixels to either region, as originally proposed by Chan and Vese in [Active Contours Without Edges, IEEE Transactions on Image Processing, 2001]. This energy is the sum of image data terms in the regions and a length penalty for region boundaries. Goldstein, Bresson and Osher modify the energy of Chan-Vese so that their new energy can be minimized efficiently using the split Bregman method to produce an equivalent two-phase segmentation. We provide a detailed implementation of this method, and document its performance with several images over a range of algorithm parameters.

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